College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 4 - Section 4.1 - Properties of Linear Functions and Linear Models - 4.1 Assess Your Understanding: 47

Answer

(a) $C(x)=90x+1800$, where $C(x)$ represents the cost (in dollars) of making $x$ bicycles in a day. (b) See the image given. (c) Cost of manufacturing $14$ bicycles a day: $C(14)=\$3060$. (d) $22$ bicycles can be manufactured for $\$3780$.
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Work Step by Step

Step-1: It is given that a linear cost function is of the form $$C(x) = mx+b$$ According to the question, the manufacturer has a fixed daily cost of $\$1800$, and it costs $\$90$ to manufacture a $single$ bicycle. Suppose the manufacturer made $4$ bicycles in a day. His cost of manufacturing will be $(90\times 4)+1800=\$2160$. Thus, replacing the bicycle quantity $4$ with a more general number, $x$, for the number of bicycles, we obtain the required cost function: $$C(x)=90x+1800$$ Step-2: Let us take values from $x=0$ to $x=4$ bicycles, to obtain the desired data points for the graph. For $C(x=0)=\$1800$ For $C(x=1)=\$1890$ For $C(x=2)=\$1980$ For $C(x=3)=\$2070$ For $C(x=4)=\$2160$ The obtained graph is given below. Step-3: $C(x=14)=(90 \times 14) + 1800 = \$3060$ Step-4: Suppose $x$ bicycles can be manufactured for $\$3780$ a day. Thus, $$3780=90x+1800$$ $$\implies 90x=3780-1800$$ $$\implies x=\frac{1980}{90}=22$$
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